{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c07c3603-0401-4196-88dc-b3992b713852",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2024-02-05 13:29:58.167206: W tensorflow/compiler/tf2tensorrt/utils/py_utils.cc:38] TF-TRT Warning: Could not find TensorRT\n",
      "WARNING:absl:GlobalAsyncCheckpointManager is not imported correctly. Checkpointing of GlobalDeviceArrays will not be available.To use the feature, install tensorstore.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Welcome to eht-imaging! v 1.2.5 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "import functools\n",
    "import os\n",
    "os.environ['CUDA_VISIBLE_DEVICES'] = '0'\n",
    "import sys\n",
    "sys.path.append('..')\n",
    "import time\n",
    "import warnings\n",
    "warnings.filterwarnings(action='ignore')\n",
    "warnings.simplefilter(action='ignore')\n",
    "\n",
    "import diffrax\n",
    "import flax\n",
    "from flax.training import checkpoints\n",
    "import IPython.display as ipd\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import optax\n",
    "\n",
    "from configs import dpi_config as dpi_config_provider\n",
    "from configs import score_config as score_config_provider\n",
    "\n",
    "import forward_models\n",
    "import probability_bound\n",
    "import probability_flow\n",
    "from posterior_sampling import model_utils as dpi_mutils\n",
    "from score_flow import utils\n",
    "from score_flow.models import utils as score_mutils\n",
    "from score_flow.models import ddpm, ncsnpp, ncsnv2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a45d78f9-beef-4580-9ae6-743250abc511",
   "metadata": {},
   "source": [
    "# Posterior Sampling with Score-based Priors: Image Denoising\n",
    "\n",
    "This notebook demonstrates how to use score-based priors for image denoising. We will use a variational-inference approach known as Deep Probabilistic Imaging (DPI) to sample from the posterior.\n",
    "\n",
    "**NOTE:** Before running, download the pre-trained CelebA score-model checkpoint from [Box](https://caltech.app.box.com/s/r9zs7oamttj64wvamjejvs4hgk9hlsuq/folder/247653500797), and save it as `../score_checkpoints/CELEBA_32/checkpoints/checkpoint_1000000`.\n",
    "\n",
    "**WARNING:** This notebook is computationally very heavy. It is recommended to start with `interferometry.ipynb`, which uses the ELBO surrogate prior. Or you can make the DPI RealNVP model smaller (e.g., by lowering `config.model.n_flow` or `config.model.seqfrac`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "602dfcc1-1db7-4b05-b79f-68f1f8ed9e6d",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "We define settings for this experiment through a `ConfigDict` for DPI.\n",
    "A `ConfigDict` for the score model is used to help load the score-based prior.\n",
    "\"\"\"\n",
    "\n",
    "# Get DPI config.\n",
    "config = dpi_config_provider.get_config()\n",
    "\n",
    "config.data.image_size = 32\n",
    "config.data.num_channels = 3\n",
    "\n",
    "config.likelihood.likelihood = 'Denoising'\n",
    "config.likelihood.noise_scale = 0.2\n",
    "\n",
    "config.model.n_flow = 32\n",
    "config.model.seqfrac = 4\n",
    "\n",
    "config.training.batch_size = 32\n",
    "config.optim.learning_rate = 2e-4\n",
    "config.optim.grad_clip = 1.\n",
    "config.optim.prior = 'ode'  # Change to 'dsm' to use probability lower bound.\n",
    "\n",
    "# Get score-model config.\n",
    "score_config = score_config_provider.get_config()\n",
    "score_config.model.beta_max = 20.\n",
    "score_config.model.nf = 64\n",
    "\n",
    "image_shape = (config.data.image_size, config.data.image_size, config.data.num_channels)\n",
    "image_dim = np.prod(image_shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "69f0ba9f-663b-417a-8620-e2b3b71377c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "We wrap the measurement simulation and measurement-likelihood functions inside\n",
    "the `forward_models.Denoising` object.\n",
    "\"\"\"\n",
    "likelihood = forward_models.Denoising(\n",
    "  scale=config.likelihood.noise_scale,\n",
    "  image_shape=image_shape)\n",
    "\n",
    "# Load true image.\n",
    "true_image = np.load('test_data/celeba_test_image.npy')\n",
    "# Simulate noisy measurements.\n",
    "meas_rng = jax.random.PRNGKey(0)\n",
    "y = likelihood.get_measurement(meas_rng, true_image[None, ...])\n",
    "naive_image = np.clip(y.reshape(image_shape), 0., 1.)\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.imshow(true_image); plt.axis('off')\n",
    "plt.title('Original')\n",
    "plt.subplot(122)\n",
    "plt.imshow(naive_image); plt.axis('off')\n",
    "plt.title('Naive');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88b22e05-c367-4490-9821-23f30469eb8a",
   "metadata": {},
   "source": [
    "## Score-based prior\n",
    "\n",
    "A trained score-based diffusion model with parameters $\\theta$ generates images from its *score-based prior*, which we denote as $p_\\theta$. Given any image $\\mathbf{x}$, we can compute $\\log p_\\theta(\\mathbf{x})$ with the *probability flow ODE*:\n",
    "\\begin{align*}\n",
    "\\frac{\\mathrm{d}\\mathbf{x}_t}{\\mathrm{d}t}&=\\mathbf{f}(\\mathbf{x}_t,t)-\\frac{1}{2}g(t)^2\\mathbf{s}_\\theta(\\mathbf{x}_t,t)\\\\\n",
    "&=:\\tilde{\\mathbf{f}}_\\theta(\\mathbf{x}_t,t),\n",
    "\\end{align*}\n",
    "where $\\mathbf{s}_\\theta$ is the learned score model, and $\\mathbf{f}(\\mathbf{x}_t,t)$ and $g(t)$ are the drift and diffusion coefficients, respectively, of the diffusion SDE.\n",
    "\n",
    "We compute the log-probability through an initial-value problem:\n",
    "\\begin{align*}\n",
    "\\log p_\\theta(\\mathbf{x})&:=\\log p_0(\\mathbf{x}) \\\\\n",
    "&= \\log p_T(\\mathbf{x}_T)+\\int_0^T\\nabla\\cdot\\tilde{\\mathbf{f}}_\\theta(\\mathbf{x}_t,t)\\mathrm{d}t,\\quad \\mathbf{x}_0=\\mathbf{x},\n",
    "\\end{align*}\n",
    "where $p_t$ is the time-dependent marginal probability distribution of $\\mathbf{x}_t$ under the diffusion SDE.\n",
    "\n",
    "In practice we solve this ODE using [Diffrax](https://docs.kidger.site/diffrax/). Here we use the Dopri5 solver with adaptive step-sizing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1f1dfe3b-fcb1-4cf1-a69c-2a78b7308eb0",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "This score-based prior was trained on 32x32 CelebA images.\n",
    "\"\"\"\n",
    "score_model_ckpt_path = '../score_checkpoints/CELEBA_32/checkpoints/checkpoint_1000000'\n",
    "\n",
    "# Get SDE.\n",
    "sde, t0 = utils.get_sde(score_config)\n",
    "\n",
    "# Initialize score model.\n",
    "score_model, _, _ = score_mutils.init_model(jax.random.PRNGKey(0), score_config)\n",
    "score_state = score_mutils.State(\n",
    "    step=0,\n",
    "    model_state=None,\n",
    "    opt_state=None,\n",
    "    ema_rate=score_config.model.ema_rate,\n",
    "    params=None,\n",
    "    params_ema=None,\n",
    "    rng=jax.random.PRNGKey(0))\n",
    "\n",
    "# Load score-model checkpoint.\n",
    "score_state = checkpoints.restore_checkpoint(score_model_ckpt_path, score_state)\n",
    "\n",
    "# Get score function based on trained score model.\n",
    "score_fn = score_mutils.get_score_fn(\n",
    "  sde,\n",
    "  score_model,\n",
    "  score_state.params_ema,\n",
    "  score_state.model_state,\n",
    "  train=False,\n",
    "  continuous=True)\n",
    "\n",
    "# Wrap probability flow ODE computations inside `probability_flow.ProbabilityFlow`.\n",
    "# We will use this to sample from the prior and, if `config.optim.prior == 'ode'`,\n",
    "# to compute log-probabilities.\n",
    "solver = diffrax.Dopri5()\n",
    "stepsize_controller = diffrax.PIDController(rtol=1e-3, atol=1e-5)\n",
    "# NOTE: it might be possible to use `diffrax.RecursiveCheckpointAdjoint`\n",
    "# instead of `BacksolveAdjoint`.\n",
    "adjoint = diffrax.BacksolveAdjoint(\n",
    "  solver=diffrax.Dopri5(),\n",
    "  stepsize_controller=diffrax.PIDController(rtol=1e-3, atol=1e-5, norm=diffrax.adjoint_rms_seminorm))\n",
    "prob_flow = probability_flow.ProbabilityFlow(\n",
    "  sde=sde,\n",
    "  score_fn=score_fn,\n",
    "  solver=solver,\n",
    "  stepsize_controller=stepsize_controller,\n",
    "  adjoint=adjoint,\n",
    "  n_trace_estimates=16)\n",
    "\n",
    "# Get function for computing ELBO, which is used if `config.optim.prior == 'dsm'`.\n",
    "bound_fn = probability_bound.get_likelihood_bound_fn(\n",
    "    sde, score_fn, image_dim,\n",
    "    dsm=True, eps=t0, N=config.optim.dsm_nt, importance_weighting=True,\n",
    "    eps_offset=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6c1a4ba9-765e-4e7e-b5f0-9fa74f21ffa4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 18 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Check ODE samples.\n",
    "\"\"\"\n",
    "z = jax.random.normal(jax.random.PRNGKey(0), (9, *image_shape))\n",
    "samples, _ = prob_flow.ode(z, sde.T, t0, dt0=None)\n",
    "utils.plot_image_grid(samples[:9]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "588db0fe-7df9-48ea-a529-47c0baac6320",
   "metadata": {},
   "source": [
    "## DPI optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "00877060-d1e0-45f5-adeb-aaa61e83ff1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Here we define the objective functions and update step for the RealNVP.\n",
    "\"\"\"\n",
    "\n",
    "sampling_shape = (config.training.batch_size // jax.local_device_count(), *image_shape)\n",
    "\n",
    "# Define data loss function (aka negative log measurement likelihood).\n",
    "def data_loss_fn(x):\n",
    "  log_likelihood = likelihood.unnormalized_log_likelihood(x, y)\n",
    "  return -jnp.mean(log_likelihood)\n",
    "\n",
    "\n",
    "# Define prior loss function (aka negative log prior).\n",
    "if config.optim.prior == 'ode':\n",
    "  logp_fn = functools.partial(prob_flow.logp_fn, t0=t0, t1=sde.T, dt0=None)\n",
    "  def prior_loss_fn(rng, x):\n",
    "    log_prior = logp_fn(rng, x)\n",
    "    return -jnp.mean(log_prior)\n",
    "elif config.optim.prior == 'dsm':\n",
    "  def prior_loss_fn(rng, x):\n",
    "    bound = bound_fn(rng, x)\n",
    "    return -jnp.mean(bound)\n",
    "\n",
    "\n",
    "def get_loss_fn(model):\n",
    "  def loss_fn(rng, params, model_state):\n",
    "    # Get samples.\n",
    "    sample_fn = dpi_mutils.get_sampling_fn(model, params, model_state, train=True)\n",
    "    rng, step_rng = jax.random.split(rng)\n",
    "    (samples, reverse_logdet), new_model_state = sample_fn(step_rng, sampling_shape)\n",
    "\n",
    "    # Data loss.\n",
    "    data_loss = data_loss_fn(samples)\n",
    "\n",
    "    # Prior loss.\n",
    "    rng, step_rng = jax.random.split(rng)\n",
    "    prior_loss = prior_loss_fn(step_rng, samples)\n",
    "\n",
    "    # Entropy loss.\n",
    "    entropy_loss = -jnp.mean(reverse_logdet)\n",
    "\n",
    "    # Total loss.\n",
    "    loss = data_loss + prior_loss + entropy_loss\n",
    "    \n",
    "    return loss, (new_model_state, samples, data_loss, prior_loss, entropy_loss)\n",
    "\n",
    "  return loss_fn\n",
    "\n",
    "\n",
    "def get_step_fn(model, optimizer):\n",
    "  loss_fn = get_loss_fn(model)\n",
    "  loss_and_grad_fn = jax.value_and_grad(loss_fn, argnums=1, has_aux=True)\n",
    "  \n",
    "  def step_fn(rng, state):\n",
    "    rng, step_rng = jax.random.split(rng)\n",
    "    (loss, (new_model_state, samples, data_loss, prior_loss, entropy_loss)), grad = loss_and_grad_fn(\n",
    "      step_rng, state.params, state.model_state)\n",
    "    grad = jax.lax.pmean(grad, axis_name='batch')\n",
    "    loss = jax.lax.pmean(loss, axis_name='batch')\n",
    "    data_loss = jax.lax.pmean(data_loss, axis_name='batch')\n",
    "    prior_loss = jax.lax.pmean(prior_loss, axis_name='batch')\n",
    "    entropy_loss = jax.lax.pmean(entropy_loss, axis_name='batch')\n",
    "\n",
    "    # Apply updates.\n",
    "    updates, new_opt_state = optimizer.update(grad, state.opt_state, state.params)\n",
    "    new_params = optax.apply_updates(state.params, updates)\n",
    "\n",
    "    step = state.step + 1\n",
    "    new_state = state.replace(\n",
    "        step=step,\n",
    "        opt_state=new_opt_state,\n",
    "        params=new_params,\n",
    "        model_state=new_model_state,\n",
    "        rng=rng)\n",
    "\n",
    "    return new_state, (loss, data_loss, prior_loss, entropy_loss), samples\n",
    "\n",
    "  return step_fn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "cf97cc06-d461-41ad-b9ef-ce08891d1d8d",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "We define a function for showing DPI optimization progress.\n",
    "\"\"\"\n",
    "def plot_dpi_progress(step, samples, losses_total, losses_data, losses_prior, losses_entropy):\n",
    "  mean = np.mean(samples, axis=0)\n",
    "  std = np.std(samples, axis=0)\n",
    "  std = np.mean(std, axis=-1)  # average std. dev. across channels\n",
    "\n",
    "  fig, axs = plt.subplots(3, 3, figsize=(20, 18))\n",
    "  fig.suptitle(f'step {step}', fontsize=20)\n",
    "\n",
    "  ax = axs[0, 0]\n",
    "  ax.plot(losses_data); ax.set_title('data loss', fontsize=18)\n",
    "\n",
    "  ax = axs[0, 1]\n",
    "  ax.plot(losses_prior); ax.set_title('prior loss', fontsize=18)\n",
    "\n",
    "  ax = axs[0, 2]\n",
    "  ax.plot(losses_entropy); ax.set_title('entropy loss', fontsize=18)\n",
    "\n",
    "  ax = axs[1, 0]\n",
    "  ax.plot(losses_total); ax.set_title('total loss', fontsize=18)\n",
    "\n",
    "  ax = axs[1, 1]\n",
    "  ax.set_title('mean', fontsize=18)\n",
    "  p = ax.imshow(np.clip(mean, 0., 1.))\n",
    "  ax.axis('off')\n",
    "  fig.colorbar(p, ax=ax)\n",
    "\n",
    "  ax = axs[1, 2]\n",
    "  ax.set_title(f'std dev (n = {len(samples)})', fontsize=18)\n",
    "  p = ax.imshow(std); ax.axis('off');\n",
    "  fig.colorbar(p, ax=ax)\n",
    "\n",
    "  for i in range(3):\n",
    "    ax = axs[2, i]\n",
    "    ax.imshow(np.clip(samples[i], 0., 1.))\n",
    "    ax.axis('off')\n",
    "    ax.set_title('sample', fontsize=18)\n",
    "\n",
    "  return fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a58a9136-ebf6-4e78-b9d5-e7bd88a652fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x1800 with 11 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time/step: 56.65 sec\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "We iteratively sample from the RealNVP, estimate its KL divergence to the target posterior,\n",
    "and update the RealNVP parameters with gradients to minimize the KL divergence.\n",
    "\"\"\"\n",
    "initialize = True\n",
    "rejit_step_fn = True  # Set to `False` to save time re-jitting step function.\n",
    "\n",
    "load_checkpoint = False\n",
    "save_ckpts = False\n",
    "ckpt_freq = 100  # Save DPI checkpoint every `ckpt_freq` steps.\n",
    "ckpt_dir = 'checkpoints/denoising'\n",
    "vis_freq = 1  # Visualize DPI progress every `vis_freq` steps.\n",
    "\n",
    "if save_ckpts:\n",
    "  os.makedirs(ckpt_dir, exist_ok=True)\n",
    "\n",
    "if initialize:\n",
    "  losses_total, losses_data, losses_prior, losses_entropy = [], [], [], []\n",
    "\n",
    "  # Initialize model.\n",
    "  model, model_state, params = dpi_mutils.get_model_and_init_params(\n",
    "      config,\n",
    "      train=True)\n",
    "  \n",
    "  # Initialize optimizer.\n",
    "  optimizer = optax.chain(\n",
    "    optax.clip_by_global_norm(config.optim.grad_clip),\n",
    "    optax.adam(\n",
    "      learning_rate=config.optim.learning_rate,\n",
    "      b1=config.optim.adam_beta1, b2=config.optim.adam_beta2,\n",
    "      eps=config.optim.adam_eps))\n",
    "  opt_state = optimizer.init(params)\n",
    "  \n",
    "  # Initialize training state.\n",
    "  state = dpi_mutils.State(\n",
    "    step=0,\n",
    "    opt_state=opt_state,\n",
    "    params=params,\n",
    "    model_state=model_state,\n",
    "    data_weight=1.,\n",
    "    prior_weight=1.,\n",
    "    entropy_weight=1.,\n",
    "    rng=jax.random.PRNGKey(config.seed + 1))\n",
    "  \n",
    "  if load_checkpoint:\n",
    "    state = flax.training.checkpoints.restore_checkpoint(ckpt_dir, state)\n",
    "  print(f'Starting from step {state.step}', flush=True)\n",
    "\n",
    "  # Replicate training state.\n",
    "  pstate = flax.jax_utils.replicate(state)\n",
    "\n",
    "if rejit_step_fn:\n",
    "  step_fn = get_step_fn(model, optimizer)\n",
    "  p_train_step = jax.pmap(jax.jit(step_fn), axis_name='batch')\n",
    "\n",
    "\n",
    "n_steps = 10000\n",
    "init_step = flax.jax_utils.unreplicate(pstate.step)\n",
    "rng = state.rng\n",
    "\n",
    "for step in range(init_step, n_steps):\n",
    "  start_time = time.perf_counter()\n",
    "\n",
    "  # Train step.\n",
    "  rng, step_rngs = utils.psplit(rng)\n",
    "  pstate, (ploss, ploss_data, ploss_prior, ploss_entropy), psamples = p_train_step(\n",
    "      step_rngs, pstate)\n",
    "\n",
    "  # Unreplicate losses, samples.\n",
    "  loss = flax.jax_utils.unreplicate(ploss).item()\n",
    "  loss_data = flax.jax_utils.unreplicate(ploss_data).item()\n",
    "  loss_prior = flax.jax_utils.unreplicate(ploss_prior).item()\n",
    "  loss_entropy = flax.jax_utils.unreplicate(ploss_entropy).item()\n",
    "  samples = psamples.reshape(config.training.batch_size, *image_shape)\n",
    "\n",
    "  # Update losses.\n",
    "  losses_total.append(loss)\n",
    "  losses_data.append(loss_data)\n",
    "  losses_prior.append(loss_prior)\n",
    "  losses_entropy.append(loss_entropy)\n",
    "\n",
    "  step_time = time.perf_counter() - start_time\n",
    "\n",
    "  if save_ckpts and ((step + 1) % ckpt_freq == 0):\n",
    "    # Save model checkpoint.\n",
    "    flax.training.checkpoints.save_checkpoint(\n",
    "      ckpt_dir,\n",
    "      flax.jax_utils.unreplicate(pstate),\n",
    "      step=step + 1,\n",
    "      keep=np.inf)\n",
    "\n",
    "  if (step + 1) % vis_freq == 0 or step == 0:\n",
    "    ipd.clear_output(wait=True)\n",
    "    fig = plot_dpi_progress(\n",
    "        step + 1, samples, losses_total, losses_data, losses_prior, losses_entropy);\n",
    "    plt.show()\n",
    "    print(f'time/step: {step_time:.2f} sec', flush=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2bc90a67-556a-467c-a731-101e0c9d1152",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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